A new survey from PNC Wealth Management found that 82 percent of American millionaires said that their kids should be responsible for creating their own wealth. That's up from 65 percent in 2007.

More than 80 percent also said that raising successful, hard-working children is their most important goal.

They want, in other words, the same middle-class childhood they had themselves. The survey found that 75 percent of the millionaires said they grew up in an "average" financial situation. Only 12 percent grew up well-off and 12 percent grew up "poor."

But when it comes the lifestyle they're actually giving their kids, millionaire parents are anything but average.

They study found that half of them are leaving their kids more than $500,000. Fully 61 percent plan to pass along a "substantial" inheritance to their kids. That's not to mention the financial support they give them along the way.

"It's a conundrum," said Stephen Pappaterra, managing director of wealth planning for PNC Wealth Management. "There does seem to be a gap. They want their kids to be responsible and self-sufficient and independent. At the same time they're dealing the practicalities of their economic situation."

Pappaterra said that wealthy parents want their kids to make it on their own, but they also know that economic opportunities today may not be as plentiful as they used to be. Hence, the need for more help. Kids today also feel more entitled to support and material comforts, he added.

"If they grew up in an affluent town, they might expect to have their college paid for, along with car payments, and other things," he said.

So while wealthy parents may want their kids to be middle class, their economic reality is decidedly different.